There are two types of vehicle wheel bearing apparatus, those for a driving wheel and those for a driven wheel. Improvements to wheel bearing apparatus have been achieved by reducing manufacturing cost and by reducing weight and size to improve fuel consumption. One representative example of such a prior art bearing apparatus is shown in FIG. 4.
The vehicle wheel bearing apparatus of FIG. 4 is a so-called third generation type and has an axial member (wheel hub) 51, an inner ring 52, an outer ring 53, and double row rolling elements (balls) 54, 54. The axial member 51 has an integrally formed wheel mounting flange 55 to mount a wheel (not shown) at one end. An inner raceway surface 51a is formed on the axial member 51 outer circumferential surface. A cylindrical portion 51b axially extends from the inner raceway surface 51a. 
The inner ring 52 is press-fitted on the cylindrical portion 51b of the axial member 51. The inner ring 52 is formed with an inner raceway surface 52a on its outer circumferential surface. The inner ring 52 is prevented from axially slipping off of the cylindrical portion 51b of the wheel hub 51 by a caulked portion 51c. The caulked portion 51c is formed by radially outwardly deforming the end of the cylindrical portion 51b of the wheel hub 51.
The outer ring 53 has an integrally formed body mounting flange 53b and double row outer raceway surfaces 53a, 53a formed on its inner circumferential surface. The double row rolling elements 54, 54 are freely rollably contained between the double row outer raceway surface 53a, 53a and the inner raceway surfaces 51a, 52a, which are arranged opposite to one another.
The thickness of cylindrical projection 56 (shown in phantom in FIG. 4), which forms a caulked portion 51c, is gradually reduced toward its tip before it is caulked radially outward. Accordingly, the thickness of the caulked portion 51c, pressing a larger end face 52b of the inner ring, is also gradually reduced toward its tip.
The caulked portion 51c is formed by plastically deforming the tip of the cylindrical projection 56 using a caulking punch. Thus, excessive pressing force is not required. Accordingly, it is possible to prevent the generation of cracks or damage in the caulked portion 51c during the caulking process and to prevent excessive enlargement of the inner diameter of the inner ring 52 which would give influence to pre-pressure and durability in rolling fatigue. (See Japanese Laid-open Patent Publication No. 272903/1998).
In order to increase the rigidity and strength of the bearing apparatus, it is necessary to assure that the axial force (pressing force) is applied to the inner ring 52. Although the axial force caused by the caulking process is different according to various versions of bearing apparatus, it is necessary to set the amount of axial deformation displacement of the inner ring 52. This assures a predetermined axial force.
Conventionally the amount of caulking is managed in accordance with the amount of axial displacement of the caulking punch. It has been found that a variation in the amount of axial deformation of the inner ring 52 is caused due to variations in the amount of caulking caused by dimensional variations in the wheel hub 51. This occurs even though the axial displacement of the caulking punch is kept at a constant amount. Accordingly, it is preferable to set the range of the amount of axial deformation of the inner ring 52 taking into consideration the amount of axial deformation of the inner ring, which assures a predetermined axial force, and variations in the amount of caulking. It is substantially impossible to set the amount of the axial deformation of the inner ring 52 while carrying out caulking tests in accordance with the versions of bearing apparatus since apparent methods of setting the amount of axial deformation of the inner ring 52 have not yet been established.
When the limit of the amount of axial deformation of the inner ring 52 is smaller than a predetermined value, the inner ring 52 cannot be axially deformed. While the inner ring 52 is strongly caulked, the thickness of the caulked portion 51c of the wheel hub 51 is reduced. Thus, the strength of the caulked portion is also reduced. On the contrary, when caulking is carried out at a caulking load larger than a predetermined caulking load, the amount of axial deformation of the inner ring 52 can be slightly increased. However, the caulking punch experiences premature abrasion or cracks by the excessive load. Thus, the working efficiency is largely reduced.